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Question

If limxax9a9xa=limx5(4+x), find all possible values of a.

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Solution

Given limxax9a9xa=limx5(4+x).....(i)

LHS=limxax9a9xa

=9(a)91=9a8........(ii)

RHS=limx5(4+x)=4+5=9.......(iii)

Subsituting (ii)and (iii)in (i),

9a8=9

a8=1

a2=1

a=1,a=1


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